The invention is in the field of amplification devices using materials having negative differential conductivity, and in particular is a planar transmission line (i.e., co-planar or slot line) comprising planar electrodes on an epitaxial layer of Gallium Arsenide. The line is biased above the Gunn threshold of the material and the n .sup.. L product is selected to suppress the formation of domains.
The activity of electromagnetic waves in solid state microwave transmission lines can be explained in terms of Maxwell's equations. See "Description of Dielectrics by Various Sets of Parameters" at pp. 9-13, of the publication "Dielectric Materials and Applications" edited by Von Hippel, MIT Press. Microwave solid state transmission lines are well known in the art and they may take such forms as planar transmission lines, microstrip, etc. Basically, such devices comprise metal conductors and an associated dielectric material. The input/output voltage relationship for a microwave transmission line is: EQU V.sub.out = V.sub.in e .sup.-.sup.j(.sup..omega./c).sup..sqroot. .sup..epsilon..sbsp.cl, (1)
where;
v.sub.in is the input voltage, PA1 v.sub.out is the output voltage, PA1 .omega. is the radian frequency of the voltage, PA1 c is the speed of light, and PA1 .epsilon..sub.c is the complex dielectric constant. PA1 Gunn effect: The exhibition of negative differential conductivity in a semiconductor having the double valley conduction band. PA1 Gunn material: A material which exhibits the Gunn effect. PA1 Gunn oscillations: The oscillations in a device exhibiting the Gunn effect when the device is biased above the Gunn threshold field. PA1 Gunn diode: A two terminal bulk semiconductor device having ohmic contacts and exhibiting Gunn oscillations. PA1 Lsa diode: A Gunn diode operated in the limited space charge accumulation mode. PA1 1. Baynham, U.S. Pat. No. 3,796,964; PA1 2. "Wave Propagation in Negative Differential Conductivity Media: n-Ge", by Baynham, IBM Journal of Research and Development, Vol. 13, No. 5, September, 1969; PA1 3. "Emission of TEM Waves Generated Within an n-Type Ge Cavity", Electron Letters, 1970, 6, pp. 306-307 by Baynham; and PA1 4. "New Mode of Microwave Emission From GaAs", Electronics Letters, Aug. 6, 1970, Vol. 6, No. 16, pp. 498-500, by Baynham and Colliver.
The term c.omega..sqroot..epsilon..sub.c is defined as the propagation constant, K, of the medium. Typically, one is looking for a transmission line which will have low loss. Consequently, perfect dielectrics are sought wherein the conductivity, .delta., approaches zero. This results in .epsilon..sub.c and K being real numbers only. The output voltage becomes: EQU V.sub.out = V.sub.in e .sup.-.sup.jKl ( 2)
Since K is a real number, the exponential is imaginary and has no real part. Consequently, the difference between V.sub.in and V.sub.out is only in the phase shift. Materials which have conductivities substantially different than zero, such as semiconductors, are lossy dielectrics and are not usually favored as transmission lines.
If one were to use a material having a differential conductivity, .delta., which is negative in the region above the Gunn threshold, the equation for V.sub.out becomes: ##EQU1##
When we take the square root of a complex term with a + j, we get a complex term having a real part, R.sub.e, and an imaginary part, +jLm. Thus, EQU V.sub.out = V.sub.in e .sup.-.sup.j(.sup..omega./c)(R.sbsp.e .sup.+ jLm)l ,
which can be written as: EQU V.sub.out = V.sub.in e .sup..alpha. .sup.l e .sup.j.sup..beta. l ,
where .alpha. is real and positive. The e .sup..alpha. .sup.l is the real part and represents amplification. It can be appreciated that the amplification increases with increased l.
The term bulk semiconductor as used herein and as used conventionally in the art, refers to a semiconductor device which does not have a barrier. For example, transistors, junction diodes, Esaki diodes, etc. are semiconductor devices whose characteristics are dependent to some extent on the barrier interface between n-type and p-type conductivity materials.
An example of a bulk semiconductor is a simple slab of silicon or germanium, or gallium arsenide, etc. Typically, when the term device is used in combination with bulk semiconductor, one is referring to some active electronic element whose characteristics depend on the properties of the bulk semiconductor material. A Gunn diode is a bulk semiconductor device. (It should be noted that the term diode simply refers to a two terminal device, no p-n junction is implied.)
A substantial amount of research in recent years has been directed toward the investigation of properties of so-called double valley semiconductors. These are semiconductors, such as GaAs and other III-V compounds, which have lower and upper conduction band valleys in momentum space separated in energy. In an article by J. B. Gunn, entitled "Instabilities of Current in III-V Semiconductors", IBM Journal of Research and Development, Vol. 8, No. 2, April, 1964 (this article is typically noted as the first publication of the Gunn effect), the author noted instabilities in the currentvoltage characteristics of III-V compounds. He noted that at some particular voltage, V.sub.T, subsequently known as the Gunn threshold, the current reaches maximum and a further voltage increase results in current instabilities. He also noted that the current fluctuations take the form of oscillations of a well defined period and are based upon the transit time of electrons between the electrodes.
Subsequent work by Gunn and others has resulted in a presently accepted explanation for the Gunn effect. See, for example, "Bulk Negative-Resistance Semiconductor Devices" by John Copeland, IEEE Spectrum, May, 1967. An oversimplified explanation will be given here to aid the reader, but for an accurate and detailed explanation reference should be made to the numerous publications in the field. Also, the explanation will be given for GaAs since most of the work has been done with that semiconductor. It will be understood that the explanation is applicable to other materials.
Reference is made to FIGS. 1 and 2 which are extracted from the above-mentioned Copeland article. FIG. 1 is a plot of the average carrier drift velocity in cm/sec .times. 10.sup.6 versus the applied electric field in kV/cm for n-type GaAs. As can be seen, the drift velocity of the carriers (electrons) decreases at electric fields above .apprxeq. 3kV/cm. The latter is known as the Gunn threshold of n-type GaAs. The explanation of the dip in the V.sub.e (drift velocity) curve is the so-called double-valley theory which Copeland attributes to Ridley, Watkins and Hilsum.
The semiconductor has lower and upper conduction band valleys, as shown in FIG. 2. These valleys are separated by 0.35 electron volts. Those electrons in the lower valley have higher mobility than those in the upper valley. At room temperature with no applied E field, almost all of the electrons are in their low energy states and the average drift velocity is zero. When a small E field is applied the electron distribution shifts so that more electrons are moving with the field than against it. The average drift velocity of the electron stream increases with increasing electric field until the fraction of electrons with energy greater than 0.35 eV begings to increase rapidly. Electrons with energy greater than 0.35 eV transfer to the more numerous states in the upper valleys where they have the same energy but much less average velocity. At the Gunn threshold, about 3,000 V/cm, the average electron drift velocity reaches a maximum value of 20 .times. 10.sup.6 cm/sec. At higher fields the electrons are mostly in the upper valleys and the average velocity decreases to a more or less constant value of 8 .times. 10.sup.6 cm/sec.
The electron mobility .mu. is dependent upon the drift velocity (.mu. = (.nu./E)) and the conductivity .delta. is dependent upon the mobility .mu.(.delta. = n.mu.e). Thus, in the region of the negative slope of the drift velocity versus field curve the bulk exhibits a negative differential mobility and a negative differential conductivity. This is often referred to as the negative resistance region of the bulk GaAs. However, as will be recalled from above, the I-V curve does not show a negative slope above the Gunn threshold; it exhibits instabilities.
Remembering that the Gunn diode is a two-terminal device consisting of two ohmic contacts to a bar or piece of n-type GaAs, or other suitable semiconductor, it will be appreciated that electrons entering the semiconductor at the negative terminal travel across the device to the positive terminal. A space charge builds up near the cathode because of the reverse dielectric-relaxation effects. In effect, electrons enter the space charge region near the cathode and emerge from the space charge region and traverse the semiconductor to the anode. Measurements by Gunn showed that as the voltage was increased past the threshold, the space charge build up becomes so great the high field domains are formed near the cathode. The cause of the space charge build up is attributed to the negative resistivity which in turn is attributed to the double valley model. The high field domains reduce the electric field in the rest of the diode and cause the current to drop to about two-thirds of the maximum value. The high field domain then drifts with the carrier stream across the sample and disappears at the anode contact. As the old domain disappears at the anode, the electride field behind it increases (to keep the voltage, .nu.Edx, constant) until the threshold field is reached and the current increases back to the threshold value. At this time a new domain forms at the cathode, the current drops, and the cycle begins anew.
An example of the current waveform thus produced is shown in FIG. 3. The flat valley occurs as the domain drifts across the sample. The upward spikes begin as a domain reaches the anode, and a new domain forms at the cathode.
The time between current pulses is .tau..sub.t, so that 1/.tau..sub.t is the fundamental frequency of oscillation of a Gunn diode. By proper biasing and control of external circuitry, a Gunn diode can be operated as an oscillator or amplifier at the fundamental frequency or at other frequencies. One other mode of operating the same type of device is known as LSA mode, and is described by Copeland in his paper "LSA Oscillator -- Diode Theory" in the Journal of Applied Physics, Vol. 38, No. 8, July, 1967.
In order to prevent confusion due to nomenclature certain terms should be cleared up. As used herein the following terms have the following meaning:
While Gunn diodes have been found useful as high frequency oscillators and amplifiers they are relatively noisy and are transit time limited. The latter means that the response of such devices drops off with increasing frequency for frequencies higher than the reciprocal of the transit time of domains from the cathode to the anode.
According to Watson, when bulk GaAs has an n .sup.. L product of .ltorsim.10.sup.12, the device may be d.c. stable and will not exhibit Gunn oscillations. The reason for this is explained in, "Microwave Semiconductor Devices and Their Circuit Applications" by Watson, McGraw Hill, 1969, pp. 501-505. Such a two-terminal device is known to exhibit amplification bands at the transit time frequency and its harmonics.
Gunn diodes are two terminal devices and are to be distinguished from transmission lines. Two terminal devices may affect a signal but there is no distinction between input and output per se. In a transmission line there are at least two ports. One at the input and one at the ouput. The voltage applied to the input port travels down the line to the ouput port. The voltage at the output port may or may not differ in amplitude and phase from the input voltage depending upon what takes place in the line. In a two-terminal device there is no distinction between input and output voltages. There are only two terminals connecting the device to the outside world and a voltage can only exist across these two terminals.
Two port devices utilizing the negative differential conductivity of GaAs to amplify microwaves have been taught by Robson, Kino and Fay in "Two-Port Microwave Amplification in Long Samples of Gallium Arsenide", IEEE Transactions on Electron Devices, Sept. 1967, pp. 612-615. In the device shown in FIG. 1, an elaborate arrangement is provided for coupling the r.f. to the bulk device. The n .sup.. L product is maintained low enough to prevent domain formation. Variations of the Robson et al amplifier design are found in Acket et al., U.S. Pat. No. 3,648,185 and Gandhi et al. U.S. Pat. No. 3,833,858. In the latter patents, different techniques are taught for suppressing domain formation. However, each has in common with Robson the feature that the microwave is coupled into the semiconductor to propagate in a direction parallel to the E field. Such devices are unilateral in operation because they operate by converting, by transducer, the microwave into a space charge, amplifying the space charge, and reconverting the amplified space charge into a microwave. Since the space charge grows only in the direction from cathode to anode, the device is unilateral (the bias field defines the cathode and anode).
A different mode of operation has been taught by Baynham in the following references:
Baynham achieves a true transmission line amplification effect in bulk semiconductor materials. The device is two-port, but unlike the Robson et al devices, the direction of propagation is perpendicular to the direction of the space charge wave. The Baynham transmission lines are microstrip transmission lines, having an n .sup.. L product below that which permits domain formation.